$A$ hydrogen atom absorbs radiation of wavelength $975 \, \mathring{A}$ and transitions from the ground state to an excited state. How many spectral lines are possible in the emission spectrum?

The electron in a hydrogen atom is initially in the second excited state. When it finally moves to the ground state, the maximum number of spectral lines emitted are:

Missing lines in a continuous spectrum reveal

In the Balmer series,the wavelength of the $2^{\text{nd}}$ line is $\lambda_1$ and for the Paschen series,the wavelength of the $1^{\text{st}}$ line is $\lambda_2$. Then the ratio $\lambda_1 : \lambda_2$ is:

In the Lyman series,the series limit of wavelength is $\lambda_1$. The wavelength of the first line of the Lyman series is $\lambda_2$ and in the Balmer series,the series limit of wavelength is $\lambda_3$. Then the relation between $\lambda_1$,$\lambda_2$,and $\lambda_3$ is

The stopping potential for the photoelectrons emitted from a metal surface of work function $1.7 \ eV$ is $10.4 \ V$. Identify the energy levels corresponding to the transitions in a hydrogen atom which will result in the emission of a wavelength equal to that of the incident radiation for the above photoelectric effect.